# Solve this system of equations: -2x + y + z = -2 5x + 3y + 3z = 71 4x -2y -3z = 1

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The following system of equations has to be solved:

-2x + y + z = -2 ...(1)

5x + 3y + 3z = 71 ...(2)

4x -2y -3z = 1 ...(3)

From (1)

y + z = -2 + 2x

and (2) gives y + z = (71 - 5x)/3

-2 + 2x = (71 - 5x)/3

=> -6 + 6x = 71 - 5x

=> 11x = 77

=> x = 7

Substitute in (1)

=> y + z = 12

=> y = 12 - z

Substitute x = 7 in (3)

2y + 3z = 27

Substitute y = 12 - z

=> 24 - 2z + 3z = 27

=> z = 3

y = 9

**The solution of the given set of equations is x = 7, y = 9 and z = 3**

-2x + y + z = -2 (i)

5x + 3y + 3z = 71 (ii)

4x -2y -3z = 1 (iii)

multiply (i)by 3 and add to (iii)

-2x+y=-5 (iv)

add (ii) to (iii)

9x+y=72 (v)

subtract (iv) from (v)

11x=77

**x=7**

put x+7 in (iv),we have

**y=9**

substitute x,y in (i) ,we have

-2.7 + 9 + z = -2

**z=3**.